hindrance; obstacle; impediment
Refers to something that gets in the way of a plan, action, or smooth progress. Often used in the phrase 差し障りがある (there is a hindrance) or 差し障りのない (harmless, inoffensive).
There is a hindrance to talking about this matter.
I chose a harmless topic.
annoyance (to others); offense; harm
Focuses on causing trouble, annoyance, or harm to others. Often used in negative constructions like 差し障りがない (causes no offense/harm).
His words caused annoyance to those around him.
Behave so as not to cause offense.